CN110456334B - TDM-MIMO radar system based on optimized sparse array and signal processing method thereof - Google Patents
TDM-MIMO radar system based on optimized sparse array and signal processing method thereof Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract
The invention discloses a TDM-MIMO radar system based on an optimized sparse array and a signal processing method thereof. The system is based on a sparse array, optimizes the array arrangement by utilizing a genetic algorithm, reduces side lobe level and improves energy utilization rate in an optimized array arrangement mode. Meanwhile, the system adopts the TDM technology to transmit the LFMCW signal, namely, the orthogonal signal is not required to be transmitted, and matched filtering at a receiving end is not required, so that the complexity of the radar system structure is further reduced. Under the condition that the number of array elements is certain, the DOA performance of the system is superior to that of the traditional uniform linear array MIMO radar system, and under the condition of the same array aperture, the system can obtain the same DOA performance as that of the uniform linear array MIMO radar system, and the angle resolution is higher and the structure is simpler. In addition, the signal calibration processing method provided by the invention can effectively improve the accuracy and resolution of DOA estimation of the system on the moving target under the condition of low signal-to-noise ratio.
Description
Technical Field
The invention belongs to the field of radar systems and signal processing, and particularly relates to a TDM-MIMO radar system based on an optimized sparse array and a signal processing method thereof.
Background
MIMO, a multiple input multiple output technology, has wide application in radar systems. Most of the MIMO radars currently adopt a structure of a uniform linear array because the uniform linear array is easy to implement. When the array structure is fixed, the array aperture of the uniform linear array structure cannot be changed, which greatly limits the practical application of the MIMO radar, and in practical application, in order to obtain a larger array aperture under the condition of limited number of antenna array elements, a sparse array is introduced into the MIMO radar. The sparse array performs sparse arrangement on the array, and compared with the traditional uniform linear array, the sparse array has fewer array elements, but can obtain higher angular resolution through reasonable arrangement, and the structure of the antenna part of the radar system can be simplified by adopting the sparse array, and higher performance is obtained.
The arrangement of the sparse array can be optimized by various means to obtain lower side lobes and narrower beams. There are various methods for optimizing, for example, the minimum redundancy optimization is to exhaust the number of array elements of the sparse array to obtain the number of the array elements with the minimum redundancy and the array element arrangement position, but when the number of the array elements is large, the exhaustion mode can make the calculation amount of the method very large; particle swarm optimization is to start from a random arrangement mode of a sparse array, select a certain variable such as an array directional diagram side lobe as an adaptability function, and then search for an optimal solution through iterative search, wherein the optimal solution is easy to sink into local optimal, so that uncertainty of the optimal solution is caused.
Conventional MIMO radars require quadrature signals to be transmitted at the transmitting end and matched filtering at the receiving end, which requires a complex design in hardware. The TDM is a Time Division Multiplexing (TDM) working mode for sending and receiving signals in a time division mode, the MIMO radar in the working mode does not need to send orthogonal signals and match filtering, and the TDM transmission adopts the TDM mode to cause the frequency deviation of echo signals when a radar system detects a moving object, so that the DOA performance of the radar system is greatly affected.
Disclosure of Invention
The invention aims to provide a radar system with simple structure, low cost and strong anti-interference capability and a signal processing method for realizing high-precision and high-resolution DOA estimation.
The technical solution for realizing the purpose of the invention is as follows: a TDM-MIMO radar system based on optimized sparse array comprises a transmitting antenna array and a receiving antenna array, wherein the transmitting antenna array comprises M transmitting array elements Tx m Interval d between transmitting array elements t W is w multiplied by lambda, w is the number of grid points uniformly distributed by the receiving antenna array; the receiving antenna array comprises N receiving array elements Rx n The specific value of N and the arrangement of the receiving array elementsThe method is obtained by combining a genetic algorithm with the number w of grid points and whether a receiving array element exists on each grid point, wherein lambda is the carrier wavelength.
The signal processing method of the TDM-MIMO radar system based on the optimized sparse array comprises the following steps:
and step 3, processing the calibrated LFMCW echo signals by using a multiple signal classification MUSIC algorithm to obtain DOA results.
Compared with the prior art, the invention has the remarkable advantages that: 1) The radar system receiving array arrangement is optimized by adopting a genetic algorithm, the optimized array arrangement mode reduces side lobe level and improves energy utilization rate, and the system can obtain better pattern performance only by modulating array intervals; 2) Compared with an annealing algorithm, a particle swarm optimization algorithm and the like, the genetic algorithm is higher in efficiency, so that the design efficiency of the whole radar system is improved; 3) Compared with the traditional radar system, the radar system adopts a mode of combining a sparse array structure with MIMO, can obtain larger array caliber under the condition of the same array element number, and can simplify the system hardware structure due to the sparse array arrangement, thereby obtaining better performance and reducing cost at the same time; 4) The radar system adopts a mode of TDM transmission of LFMCW signals, does not need to transmit orthogonal signals, or performs matched filtering at a receiving end, thereby reducing the complexity of the radar system structure and having the characteristics of strong anti-interference capability and the like; 5) The radar system carries out frequency offset and phase error correction on the received LFMCW echo signals, so that the DOA performance of the system can be greatly improved, and the system can realize high-precision and high-resolution DOA estimation based on a MUSIC algorithm.
The invention is described in further detail below with reference to the accompanying drawings.
Drawings
Fig. 1 is a schematic diagram of an array structure and an equivalent virtual array model of a TDM-MIMO radar system based on an optimized sparse array.
Fig. 2 is a schematic diagram of a transmission mode of the radar system according to the present invention.
FIG. 3 is a schematic diagram of an iterative process of a genetic algorithm in an embodiment of the present invention.
Fig. 4 is a schematic diagram of an arrangement of receiving array elements after genetic algorithm optimization in an embodiment of the present invention.
FIG. 5 is a comparison of array patterns for optimized and un-optimized systems in accordance with an embodiment of the present invention.
FIG. 6 is a graph of DOA results for an uncorrected radar system to detect stationary targets in an embodiment of the present invention.
Fig. 7 is a diagram of FFT results and DOA results of a radar system detecting a moving object before correction in an embodiment of the present invention, where (a) is the FFT result diagram and (b) is the DOA result diagram.
Fig. 8 is a diagram of FFT results and DOA results of a radar system detecting a moving object after correction according to an embodiment of the present invention, where (a) is the FFT result diagram and (b) is the DOA result diagram.
Fig. 9 is a graph of the DOA results of the corrected radar system according to the embodiment of the present invention under different signal-to-noise ratio conditions, where graph (a) is the DOA result under SNR 1=15 dB, graph (b) is the DOA result under SNR 2=10 dB, graph (c) is the DOA result under SNR 3=5 dB, and graph (d) is the DOA result under SNR 4=0 dB.
Fig. 10 is a graph showing the comparison of mean square error before and after calibration of the radar system according to the embodiment of the present invention.
Detailed Description
Referring to fig. 1, a TDM-MIMO radar system based on an optimized sparse array includes a transmitting antenna array and a receiving antenna array, where the transmitting antenna array includes M transmitting array elements Tx m Interval d between transmitting array elements t W is w multiplied by lambda, w is the number of grid points uniformly distributed by the receiving antenna array; the receiving antenna array comprises N receiving array elements Rx n The specific numerical value of N and the arrangement mode of the receiving array elements are obtained by combining a genetic algorithm with the number w of the grid points and whether the receiving array elements exist on each grid point, wherein lambda is the carrier wavelength.
Further, the specific numerical value of N and the arrangement mode of the receiving array elements are obtained by combining a genetic algorithm with the number w of grid points and solving whether the receiving array elements exist on each grid point, specifically:
step 3, reserving the optimal fitness value of each generation and the gene strings of the optimal individuals, and selecting whether the non-optimal individual gene strings are inherited to the next generation according to a roulette method;
and obtaining the value of N according to the optimal arrangement mode.
For example, m= 2,w =20, based on w, n=12 is obtained by solving a genetic algorithm, and the arrangement mode of the receiving array elements is specifically as follows: 110000101111111100111101.
the signal processing method of the TDM-MIMO radar system based on the optimized sparse array comprises the following steps:
and step 3, processing the calibrated LFMCW echo signals by using a multiple signal classification MUSIC algorithm to obtain DOA results.
Further preferably, the LFMCW signal in step 1 is specifically a triangular frequency modulated signal.
Further, in step 2, the LFMCW echo signal is calibrated, specifically:
step 2-1, acquiring an LFMCW echo signal according to an LFMCW standard signal and TDM, and acquiring a frequency offset term generated by the target motion;
step 2-2, eliminating frequency offset items in LFMCW echo signals by using a method based on time stretching transformation, and eliminating Doppler fuzzy factors;
and 2-3, eliminating phase errors by using an FFT-based method, and obtaining a calibrated LFMCW echo signal.
Further, step 2-1 obtains LFMCW echo signals according to LFMCW standard signals and TDM, and obtains frequency offset terms generated by target motion, specifically:
step 2-1-1, acquiring an LFMCW echo signal of an LFMCW signal transmitted by a TDM-MIMO radar system of an optimized sparse array in a TDM mode, wherein the LFMCW echo signal comprises:
(1) For the mth transmitting array element Tx m Acquiring an nth receiving array element Rx n Received signal and transmitting array element Tx m Time delay tau between transmitted signals mn ：
Wherein R is 0 For the target initial position, m=0, 1, n=0, 1,..11, w mn ＝(m·N·d r +n·d rn )sinθ；d r To receive array grid point spacing, d rn For receiving the interval between array elements, θ is the incidence angle of the target echo signal; t is a frequency modulation period; mT is the actual slow time; t is a fast time; assuming that the target moves at a uniform speed, wherein the movement speed is v, and setting the direction of the target away from the radar to be positive; c is the speed of light;
(2) The time delay tau is set mn Substituting the signal into LFMCW standard echo signals, and combining v/c < 1 to obtain the (v/c) signal 2 ，(w mn /c) 2 And w mn /c 2 The term is ignored, and the LFMCW echo signal is obtained as follows:
in the Doppler frequency f d ＝2vf 0 /c；F＝1/T；f d rF represents the frequency of blurring due to doppler effect, r is the doppler blurring factor; a is the amplitude of a transmitted signal; a is that 0 For the amplitude of echo signals, A 0 The magnitude of (a) is related to the gain of the receiver antenna, the distance between the radar and the target, the reflective cross-sectional area of the target, etc.; f (f) 0 Is carrier frequency; τ 0 Time delay for the initial position of the target; k=b/T is the slope of the fm signal, B is the fm signal bandwidth;
wherein, LFMCW standard echo signal:
and 2-1-2, comparing the LFMCW echo signal with the LFMCW standard echo signal to obtain a frequency offset term exp (2 kmvTt/c).
Further, step 2-2 uses a method based on time stretching transformation to eliminate frequency offset term in LFMCW echo signal and Doppler fuzzy factor, specifically:
step 2-2-1, establishing a relation between an actual slow time mT and a virtual slow time m' T in the LFMCW echo signal:
namely:
step 2-2-2, will
Substituting the LFMCW echo signals into LFMCW echo signals to obtain LFMCW echo signals with eliminated frequency offset terms: />
Step 2-2-3, based on step 2-2-2, using a cancellation factor
Doppler fuzzy factor in LFMCW echo signal after eliminating the frequency offset term
Obtaining Doppler blur factor eliminationThe following LFMCW echo signal:
further, step 2-3 eliminates the phase error by using the FFT-based method to obtain the calibrated LFMCW echo signal, specifically:
step 2-3-1, processing the LFMCW echo signals obtained in step 2-2-3 by utilizing FFT;
step 2-3-2, obtaining the respective frequency spectrum positions of all detection targets through spectrum peak searching;
step 2-3-3, multiplying the amplitude of the target spectrum position and the N+1 spectrum position points before and after the target by the corresponding correction coefficient
N is the target number, and finally the calibrated LFMCW echo signal is obtained:
the present invention will be described in further detail with reference to examples.
Examples
The TDM-MIMO radar system based on the optimized sparse array in the embodiment comprises a transmitting antenna array and a receiving antenna array, wherein the transmitting antenna array comprises 2 transmitting array elements Tx m Interval d between transmitting array elements t 20 x lambda; the receiving antenna array comprises N receiving array elements Rx n The specific value of N and the arrangement mode of the receiving array elements are obtained by combining a genetic algorithm with the number of the grid points 20 and whether the receiving array elements exist on each grid point, wherein lambda is the carrier wavelength. With reference to fig. 3, the genetic algorithm is optimized to obtain the lowest peak sidelobe level through 188 iterations, and the obtained number n=12 of receiving array elements optimized by the genetic algorithm is arranged in a receiving array manner shown in fig. 4. The array pattern optimized by genetic algorithm is compared with the non-optimized result such asAs shown in fig. 5, the optimized peak sidelobes are lower, while the main lobe width is similar to the original beam.
The present invention is simulated and verified as follows. Setting carrier frequency f 0 Frequency modulation period t=20ms, frequency modulation signal bandwidth b=100 MHz, sampling frequency f s =50khz. Assuming that two targets exist, the distance, speed, angle and signal-to-noise ratio are r respectively 1 ＝250m，r 2 ＝200m；v 1 ＝0m/s,v 2 ＝0m/s；θ 1 ＝25°,θ 2 ＝30°；SNR＝10dB。
DOA estimation test is carried out on an uncalibrated system signal, the result of DOA estimation by using the MUSIC algorithm is shown in figure 6, and the result is accurate at the moment, because the target is stationary at the moment, namely, the speed is 0; when the target has a speed, the angle and the speed are respectively changed to theta 1 ＝25°,θ 2 ＝27°；v 1 ＝35m/s,v 2 As can be seen from fig. 7, the frequency point of the FFT is shifted by 35m/s, and the DOA estimation result indicates that only 1 target can be detected at this time, and the error is large. The system calibrated by the method is tested, the FFT and DOA estimation results are shown in figure 8, and the frequency point after FFT is not offset any more, so that the DOA estimation results of the two targets are very accurate.
In order to more fully test the system of the invention, the DOA performance of the system under different signal to noise ratio conditions is tested next. As shown in fig. 9, for the system of the present invention, the speed is changed to v under the conditions of SNR 1=15 dB, snr2=10 dB, snr3=5 dB, snr4=0 dB 1 ＝35m/s,v 2 =35 m/s, angle change to θ 1 ＝25°,θ 2 The DOA results of the two targets of 30 degrees are very accurate, and the DOA performance of the system is proved. The mean square error of DOA estimation of the system after calibration of the invention under SNR=0-15 dB is compared with that of the uncalibrated system, as shown in figure 10, the mean square error of the system after calibration is reduced by about 90%, which proves the effectiveness of the calibration method in the invention.
The DOA performance of the radar system is superior to that of the traditional uniform linear array MIMO radar system, and the system can obtain the same DOA performance as that of the uniform linear array MIMO radar system under the same array aperture, and the angle resolution is higher. In addition, the signal calibration processing method provided by the invention can effectively improve the accuracy and resolution of DOA estimation of the system on the moving target under the condition of low signal-to-noise ratio.
Claims (7)
1. The signal processing method of the TDM-MIMO radar system based on the optimized sparse array is characterized by comprising the following steps of:
step 1, a TDM-MIMO radar system adopts a TDM mode to transmit a linear frequency modulation continuous wave LFMCW signal;
step 2, calibrating the LFMCW echo signal; the method comprises the following steps:
step 2-1, acquiring an LFMCW echo signal according to an LFMCW standard signal and TDM, and acquiring a frequency offset term generated by the target motion;
step 2-2, eliminating frequency offset items in LFMCW echo signals by using a method based on time stretching transformation, and eliminating Doppler fuzzy factors;
step 2-3, eliminating phase errors by using an FFT-based method, and obtaining a calibrated LFMCW echo signal;
step 3, processing the calibrated LFMCW echo signals by using a multiple signal classification MUSIC algorithm to obtain DOA results;
the TDM-MIMO radar system comprises a transmitting antenna array and a receiving antenna array, wherein the transmitting antenna array comprises M transmitting array elements Tx m Interval d between transmitting array elements t W is w multiplied by lambda, w is the number of grid points uniformly distributed by the receiving antenna array; the receiving antenna array comprises N receiving array elements Rx n The specific numerical value of N and the arrangement mode of the receiving array elements are obtained by combining a genetic algorithm with the number w of the grid points and whether the receiving array elements exist on each grid point, wherein lambda is the carrier wavelength.
2. The signal processing method of the optimized sparse array-based TDM-MIMO radar system according to claim 1, wherein the specific value of N and the arrangement mode of the receiving array elements are obtained by combining a genetic algorithm with the number w of grid points and whether there is a receiving array element solution on each grid point, specifically:
step 1, representing an individual gene string by binary codes, and representing the existence or nonexistence of a receiving array element on a grid point by 1 and 0, wherein the form of the individual gene string is as '10001'; then randomly generating an initial population, an initial cross probability, an initial variation probability and initial iteration times according to the grid point number w;
step 2, taking peak sidelobe level in the directional diagram as a fitness function, substituting each individual gene string into the fitness function, calculating a corresponding fitness value, and selecting the individual gene string with the smallest fitness value as an optimal individual gene string;
step 3, reserving the optimal fitness value of each generation and the gene strings of the optimal individuals, and selecting whether the non-optimal individual gene strings are inherited to the next generation according to a roulette method;
step 4, randomly generating genes of each individual gene string, judging whether the generation probability of each gene is larger than the crossover probability, if so, crossing the genes, otherwise, not crossing the genes;
step 5, randomly generating genes of each individual gene string, judging whether the generation probability of each gene is larger than the variation probability, if so, the genes are mutated, otherwise, the genes are not mutated;
step 6, judging whether the maximum iteration times or the optimal fitness value is not changed by taking the set maximum iteration times and the optimal fitness value change rate as loop termination conditions, if so, terminating iteration, and taking an individual gene string with the optimal fitness as a global optimal solution, namely an optimal arrangement mode of sparse array elements;
and obtaining the value of N according to the optimal arrangement mode.
3. The signal processing method of the TDM-MIMO radar system based on the optimized sparse array according to claim 1 or 2, wherein the m= 2,w =20, based on w, is obtained by solving a genetic algorithm to obtain n=12, and the arrangement mode of the receiving array element is specifically as follows: 110000101111111100111101.
4. the signal processing method of the optimized sparse matrix-based TDM-MIMO radar system according to claim 1, wherein in step 1, the LFMCW signal specifically uses a triangular wave frequency modulation signal.
5. The signal processing method of the optimized sparse matrix-based TDM-MIMO radar system according to claim 1, wherein in step 2-1, LFMCW echo signals are obtained according to LFMCW standard signals and TDM, and frequency offset terms generated due to target motion are obtained, specifically:
step 2-1-1, acquiring an LFMCW echo signal of an LFMCW signal transmitted by a TDM-MIMO radar system of an optimized sparse array in a TDM mode, wherein the LFMCW echo signal comprises:
(1) For the mth transmitting array element Tx m Acquiring an nth receiving array element Rx n Received signal and transmitting array element Tx m Time delay tau between transmitted signals mn ：
Wherein R is 0 For the target initial position, m=0, 1, n=0, 1,..11, w mn ＝(m·N·d r +n·d rn )sinθ；d r To receive array grid point spacing, d rn For receiving the interval between array elements, θ is the incidence angle of the target echo signal; t is a frequency modulation period; mT is the actual slow time; t is a fast time; assuming that the target moves at a uniform speed, wherein the movement speed is v, and setting the direction of the target away from the radar to be positive; c is the speed of light;
(2) The time delay tau is set mn Substituting the signal into LFMCW standard echo signals, and combining v/c < 1 to obtain the (v/c) signal 2 ，(w mn /c) 2 And w mn /c 2 The term is ignored, and the LFMCW echo signal is obtained as follows:
in the Doppler frequency f d ＝2vf 0 /c；F＝1/T；f d rF represents the frequency of blurring due to doppler effect, r is the doppler blurring factor; a is the amplitude of a transmitted signal; a is that 0 For the amplitude of echo signals, A 0 The magnitude of (a) is related to the gain of the receiver antenna, the distance between the radar and the target, the reflective cross-sectional area of the target, etc.; f (f) 0 Is carrier frequency; τ 0 Time delay for the initial position of the target; k=b/T is the slope of the fm signal, B is the fm signal bandwidth;
wherein, LFMCW standard echo signal:
and 2-1-2, comparing the LFMCW echo signal with an LFMCW standard echo signal to obtain a frequency offset term exp (2 kmvT/c).
6. The signal processing method of the optimized sparse matrix-based TDM-MIMO radar system according to claim 1, wherein the method of step 2-2 of using the time-based stretching transformation eliminates the frequency offset term in the LFMCW echo signal and eliminates the doppler ambiguity factor specifically includes:
step 2-2-1, establishing a relation between an actual slow time mT and a virtual slow time m' T in the LFMCW echo signal:
namely:
step 2-2-2,Will be
Substituting the LFMCW echo signals into LFMCW echo signals to obtain LFMCW echo signals with eliminated frequency offset terms:
step 2-2-3, based on step 2-2-2, using a cancellation factor
Doppler blurring factor +.f in LFMCW echo signal after eliminating the frequency offset term>
Obtaining LFMCW echo signals after Doppler fuzzy factor elimination:
7. the signal processing method of the optimized sparse matrix-based TDM-MIMO radar system according to claim 1, wherein the step 2-3 of removing the phase error by using the FFT-based method, and obtaining the calibrated LFMCW echo signal specifically includes:
step 2-3-1, processing the LFMCW echo signals obtained in step 2-2-3 by utilizing FFT;
step 2-3-2, obtaining the respective frequency spectrum positions of all detection targets through spectrum peak searching;
step 2-3-3, multiplying the amplitude of the target spectrum position and the N+1 spectrum position points before and after the target by the corresponding correction coefficient
Wherein N is the target number, and finally the calibration is obtainedLFMCW echo signal of (b):
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| CN113204017B (en) * | 2021-03-16 | 2022-11-04 | 西安电子科技大学 | LFMCW-based MIMO radar signal processing method |
| CN113176540B (en) * | 2021-04-25 | 2022-04-19 | 南京航空航天大学 | Method and system for synthesizing sparse array MIMO radar combined beam pattern |
| CN113311404B (en) * | 2021-05-27 | 2023-01-31 | 电子科技大学长三角研究院(衢州) | MIMO radar real-time angular resolution improvement method |
| CN113343588B (en) * | 2021-07-06 | 2022-11-08 | 东南大学 | Method and device for designing multi-constraint millimeter wave vehicle-mounted MIMO radar antenna array |
| CN113671449A (en) * | 2021-07-16 | 2021-11-19 | 西安电子科技大学 | MIMO radar sidelobe interference suppression method based on minimum redundant linear array |
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| CN102208934A (en) * | 2011-06-24 | 2011-10-05 | 北京理工大学 | Antenna selection method based on full cross weight genetic algorithm |
| DE102013209708A1 (en) * | 2013-05-24 | 2014-11-27 | Robert Bosch Gmbh | Method for operating a MIMO radar |
| CN105426578B (en) * | 2015-11-03 | 2018-06-19 | 电子科技大学 | A kind of MIMO-SAR planar array element position optimization methods based on genetic algorithm |
| CN107171774A (en) * | 2017-04-14 | 2017-09-15 | 南京邮电大学 | The pilot frequency optimization method of extensive mimo system compressed sensing channel estimation |
| CN108037498B (en) * | 2017-11-16 | 2021-09-03 | 南京理工大学 | High-speed target speed and distance measuring method based on triangular wave linear frequency modulation continuous wave radar |
| CN108388718B (en) * | 2018-02-08 | 2021-07-13 | 北京理工睿行电子科技有限公司 | Optimized MIMO radar antenna array design method |
| CN109001698B (en) * | 2018-08-27 | 2022-08-23 | 北京理工大学 | Linearity calibration method for small depth-of-field linear frequency modulation continuous wave radar |
| CN109188355B (en) * | 2018-09-14 | 2023-05-02 | 四川大学 | Method for optimizing and optimally distributing receiving antennas of multi-point positioning system |
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